Re: [1 paradox]

He will accept 1 / 3 doing the division = .3333333... But he will not accept the multiplication, I am forcing him to.

Hi

That is because you do not have enough digits of precision.

Exactly! .3333333333333333 < .33333333333...

As you multiply you are going to have to admit that .9999999 eventually will become .99999999...This is just notation. You cannot think that 1 / 3 = .333333333... and that .999999999... does not exist.

In mathematics, you don't understand things. You just get used to them.

Re: [1 paradox]

Actually, 0.999999 will eventually become 1. Everywhere you write 0.999..., 1is also a valid figure.

Here lies the reader who will never open this book. He is forever dead.Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and PunishmentThe knowledge of some things as a function of age is a delta function.

Re: [1 paradox]

Now you are talking. .99999999... = 1

Here is a question none of them could deal with. If .99999999... does not equal one then what does it equal? It is obvious it keeps approaching one but like Zeno they do not believe it will ever arrive.

In mathematics, you don't understand things. You just get used to them.

Re: [1 paradox]

If it existed, it would be 1. But, I still banish it from maths. It is needless.

Here lies the reader who will never open this book. He is forever dead.Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and PunishmentThe knowledge of some things as a function of age is a delta function.

Re: [1 paradox]

It is not a definition. Can you prove the existence of 0.999...? No!

Here lies the reader who will never open this book. He is forever dead.Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and PunishmentThe knowledge of some things as a function of age is a delta function.

Re: [1 paradox]

Why won't a number exist?

did I ever say that 1 and 2 does not exist?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.''God exists because Mathematics is consistent, and the devil exists because we cannot prove it''But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

Re: [1 paradox]

0.999... is only equal to 1 because we humans made rules stating it is. I'd like to see you prove 0.999... = 1 without those rules.

For example. Take a common non-calculus proof.

1/3 = 0.333...0.333... * 3 = 0.999...1/3 * 3 = 1∴ 0.999... = 1

That explodes on the first line. 0.333... is not exactly equal to 1/3. It is the closest Base 10 number to 1/3. 1/3 is in fact: 0.333... + 1/∞*3. This proof was made to trick people into believing 0.999... = 1 without calculus proofs.Now lets rewrite that proof.

Calculus tells us that the limit of 1/x as x goes to infinity is 0, but that's calculus. It was practically made for answering this. Can you prove that "1/∞ = 0" without those rules?

Almost all people say 0.000...1 (1/∞) is 0 because you'd never write that 1 down. Why would this be? There are infinite numbers between 0 and 1, but 1 still exists. This is a concept, an idea, not a physical object. To apply physical-object ideas to a concept would be reification.

I will say this again.0.999... is equal to 1 ONLY BECAUSE we humans made extra rules saying it is. It is not equal to 1 without those rules.

Re: [1 paradox]

Hi;

1/3 = 0.333... + 1/∞*3

I am afraid that is not correct.

1/3 = .333333333... easily proved by long division.

BECAUSE we humans made extra rules saying it is

The aliens also think .99999999... = 1.

I am not supposed to release this to the public because it is still A.T.S. but here is an authentic picture of the leader of the reptilian mother ship giving a lecture at the Nevada test site on June 3, 1941.

Using this advanced alien knowledge we were able to defeat the Axis powers in the coming war ( WWII ). I was proud to have been the one that asked Reppy, " that is what he was affectionately called by his friends" what .999999... really equaled.

I remember it as if it were yesterday because Albert Einstein was sitting next to me, I remember because he had eaten garlic and he patted me on the back for my good question.

Last edited by bobbym (2013-03-21 22:15:36)

In mathematics, you don't understand things. You just get used to them.

Re: [1 paradox]

I don't know how to put this in a way you can understand, but it's generally accepted that 0.999... + 1/∞ = 1, people just choose to believe 1/∞ = 0. So we can use this equation to prove the value of 1/3.

So to sum this up in words:A third is equal to point three repeating plus a third of an infinitesimal, which sounds absurd, but it's true. Base 10 isn't perfect cause it's a round number. There's always a flaw. But it's too late to change number systems easily, so we just have to deal with these flaws.

Re: [1 paradox]

I don't know if somebody already said this, but saying that .999...≠1 implies that there is a number between .999... and 1 that is distinct from both of them. There is not.Also, the sum from n=1 to infinity of 9(1/10)^n = 1. But that's beside the point and not a very intuitive proof.

Re: [1 paradox]

hi ncik

Excellent points. And totally relevent. If mathematicians want to give a meaning to 0.9999..... then it is essential to consider what properties it would have. Once 'you' have a water-tight definition it is 'safe' to go ahead and define what it means, knowing that there are no chinks where someone can drive through an objection.

Bob

Children are not defined by school ...........The FonzYou cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Re: [1 paradox]

Hello guys;i totally agree with Bobbym...since infinity is no real number and since its value is not known,arithmetic of infinity cannot be performed as we do in case of other numbers.....

And 0.9999999999999.....can never be equal to unity.....limit of .999999..... could be 1but saying that .99999999...itself is equal to 1 would be absurd since both of those numbers have their own existence which cannot be equated......